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Explores the concept of fractions of rings and their uniqueness in ideals and quotients.
Introduces projective plane curves, degrees, components, multiplicities, intersection numbers, tangents, and multiple points, culminating in the statement of Bézout's theorem and its consequences.
Explores the construction of the field of rational functions on a variety and its connection with local rings and dimensions.
Covers the addition of fractions and properties of rational numbers, emphasizing associativity and summing fractions with the same denominator.
Covers local Noetherian rings, integrally closed domains, discrete valuations, and fraction fields.
Explains the conversion process from fractions to decimal numbers and vice versa.
Covers integers, rings, subrings, invertibility, divisors of zero, and equivalence relations in formal fractions.
